<PRE><B>Question 5302</B>
 x^2+y=31..(1)
 y^2+x=41...(2)

 From (1): y = 31-x^2
 Goto (2), we get (31-x^2)^2 + x = 41 
 or x^4 - 62x^2 + x + 920 = 0

 Use synthetic division
 1 + 0 - 62 + 1 + 920 (5
   + 5 + 25 -185 -920
 --------------------
 1 + 5 - 37 -184 + 0

 After factoring, (x-5)(x^3 + 5x^2 -37x -184) = 0.

 When x = 5 and y = 31 -25 = 6

 However, the solutions of x^3 + 5x^2 -37x -184 = 0.
 are very complicated. (1 real, two complex, try to use Cardan formula)
 
 So, here I just give you one solution.

 Kenny

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